The Deadman Wonderland anime has some deviations from the manga. Some storylines are condensed or changed to fit the animation format. But it still retains the core elements of the manga.
I'm not entirely sure specifically what 'Showtime 1996 Bedtime Stories' is about. It could be a collection of bedtime stories presented in 1996 on Showtime. Maybe it features various fictional tales for kids to listen to before going to sleep.
To be honest, I don't have a definite answer. Sometimes shows take elements from real life and fictionalize them. It's hard to say for this one without more information.